viii PRACTICAL MATHEMATICS 



CHAPTER V 



PAGE 



The Position of a Point in Space . ... 61 



The Straight Line and its direction Cosines .... 64 



The Plane .......... 70 



CHAPTER VI 



The Slope of a Line and the Slope of a Curve ... 79 



Differentiation ......... 82 



CHAPTER VII 



Successive Differentiation ....... 99 



Taylor's Expansion . ..... 103 



Maclaurin's Theorem ........ 107 



CHAPTER VIII 



Maxima and Minima ........ 115 



CHAPTER IX 



Tangent and Normal to a Given Curve . . . .130 



Curvature and Radius of Curvature ..... 134 



Centre of Curvature . . . . . . . .136 



Point of Inflexion . . ...... 139 



CHAPTER X 



Integration using Partial Fractions . . . . . 143 



f dX f dX , f dX 



The Integrals J X2 + ^ J x .,_ A2 , and J pr^xi 



f 



The Integrals 



CHAPTER XI 



dX 



